Extension of the unsymmetric 8-node hexahedral solid element US-ATFH8 to geometrically nonlinear analysis

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Zhi Li ◽  
Song Cen ◽  
Chenfeng Li
Keyword(s):  
Nonlinear Analysis ◽  
Linear Elasticity ◽  
Analytical Solutions ◽  
Geometrically Nonlinear ◽  
Governing Equations ◽  
Geometrically Nonlinear Analysis ◽  
Content Type ◽  
Solid Element ◽  
Key Innovation ◽  
Updated Lagrangian

Purpose The purpose of this paper is to extend a recent unsymmetric 8-node, 24-DOF hexahedral solid element US-ATFH8 with high distortion tolerance, which uses the analytical solutions of linear elasticity governing equations as the trial functions (analytical trial function) to geometrically nonlinear analysis. Design/methodology/approach Based on the assumption that these analytical trial functions can still properly work in each increment step during the nonlinear analysis, the present work concentrates on the construction of incremental nonlinear formulations of the unsymmetric element US-ATFH8 through two different ways: the general updated Lagrangian (UL) approach and the incremental co-rotational (CR) approach. The key innovation is how to update the stresses containing the linear analytical trial functions. Findings Several numerical examples for 3D structures show that both resulting nonlinear elements, US-ATFH8-UL and US-ATFH8-CR, perform very well, no matter whether regular or distorted coarse mesh is used, and exhibit much better performances than those conventional symmetric nonlinear solid elements. Originality/value The success of the extension of element US-ATFH8 to geometrically nonlinear analysis again shows the merits of the unsymmetric finite element method with analytical trial functions, although these functions are the analytical solutions of linear elasticity governing equations.

Application of Groebner Basis Methodology to Nonlinear Static Cable Analysis

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Y. Jane Liu ◽  
George R. Buchanan ◽  
John Peddieson
Keyword(s):  
Nonlinear Analysis ◽  
Analytical Solutions ◽  
Geometrically Nonlinear ◽  
Large Deflections ◽  
Groebner Basis ◽  
Governing Equations ◽  
Geometrically Nonlinear Analysis ◽  
Exact Analytical Solutions ◽  
Highly Nonlinear ◽  
Nonlinear Static

The governing equations for large deflections of cables have a highly nonlinear and coupled nature, which precludes exact analytical solutions except in a few simplified cases. The present study demonstrates the utility of Groebner Basis methodology in facilitating the construction of approximate analytical and semianalytical Galerkin solutions in the geometrically nonlinear analysis of cable statics.

Geometrically nonlinear analysis by the generalized finite element method

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Lorena Leocádio Gomes ◽  
Felicio Bruzzi Barros ◽  
Samuel Silva Penna ◽  
Roque Luiz da Silva Pitangueira
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Nonlinear Analysis ◽  
Geometrically Nonlinear ◽  
Generalized Finite Element Method ◽  
Geometrically Nonlinear Analysis ◽  
Content Type ◽  
Lagrangian Formulations ◽  
Updated Lagrangian ◽  
Element Method

Purpose The purpose of this paper is to evaluate the capabilities of the generalized finite element method (GFEM) under the context of the geometrically nonlinear analysis. The effect of large displacements and deformations, typical of such analysis, induces a significant distortion of the element mesh, penalizing the quality of the standard finite element method approximation. The main concern here is to identify how the enrichment strategy from GFEM, that usually makes this method less susceptible to the mesh distortion, may be used under the total and updated Lagrangian formulations. Design/methodology/approach An existing computational environment that allows linear and nonlinear analysis, has been used to implement the analysis with geometric nonlinearity by GFEM, using different polynomial enrichments. Findings The geometrically nonlinear analysis using total and updated Lagrangian formulations are considered in GFEM. Classical problems are numerically simulated and the accuracy and robustness of the GFEM are highlighted. Originality/value This study shows a novel study about GFEM analysis using a complete polynomial space to enrich the approximation of the geometrically nonlinear analysis adopting the total and updated Lagrangian formulations. This strategy guarantees the good precision of the analysis for higher level of mesh distortion in the case of the total Lagrangian formulation. On the other hand, in the updated Lagrangian approach, the need of updating the degrees of freedom during the incremental and iterative solution are for the first time identified and discussed here.

Application of Groebner Basis Methodology to Nonlinear Analysis of an Underwater Cable

2011 ◽  
Author(s):  
Y. Jane Liu ◽  
George R. Buchanan
Keyword(s):  
Galerkin Method ◽  
Nonlinear Analysis ◽  
Analytical Solutions ◽  
Large Deflection ◽  
Geometrically Nonlinear ◽  
Groebner Basis ◽  
Governing Equations ◽  
Geometrically Nonlinear Analysis ◽  
Highly Nonlinear ◽  
The Galerkin Method

The governing equations for a large deflection cable analysis have a highly nonlinear and coupled nature. As a result, analytical solutions are unavailable or limited to a few simplified cases. The present study is to apply the Groebner Basis methodology combined with the Galerkin method to a geometrically nonlinear analysis of an underwater cable as an example.

Geometrically nonlinear analysis of thick orthotropic plates with various geometries using simple HP-cloud method

2016 ◽  
Vol 33 (5) ◽  
pp. 1451-1471 ◽  
Author(s):  
Nasrin Jafari ◽  
Mojtaba Azhari
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Analysis ◽  
Large Deformation ◽  
Deformation Analysis ◽  
Geometrically Nonlinear ◽  
Orthotropic Plates ◽  
General Shape ◽  
Geometrically Nonlinear Analysis ◽  
Content Type ◽  
Large Deformation Analysis

Purpose – The purpose of this paper is to present a simple HP-cloud method as an accurate meshless method for the geometrically nonlinear analysis of thick orthotropic plates of general shape. This method is used to investigate the effects of thickness, geometry of various shapes, boundary conditions and material properties on the large deformation analysis of Mindlin plates. Design/methodology/approach – Nonlinear analysis of plates based on Mindlin theory is presented. The equations are derived by the Von-Karman assumption and total Lagrangian formulations. Newton-Raphson method is applied to achieve linear equations from nonlinear equations. Simple HP-cloud method is used for the construction of the shape functions based on Kronecker-δ properties, so the essential boundary conditions can be enforced directly. Shepard function is utilized for a partition of unity and complete polynomial is used as an enrichment function. Findings – The suitability and efficiency of the simple HP-cloud method for the geometrically nonlinear analysis of thin and moderately thick plates is studied for the first time. Large displacement analysis of various shapes of plates, rectangular, skew, trapezoidal, circular, hexagonal and triangular with different boundary conditions subjected to distributed loading are considered. Originality/value – This paper shows that the simple HP-cloud method is well suited for the large deformation analysis of Mindlin plates with various geometries, because it uses a set of a few arbitrary nodes placed in a plate of general shape. Moreover the convergence rate of the proposed method is high and the cost of solving equations is low.

Geometrically nonlinear analysis of functionally graded plates using isogeometric analysis

2015 ◽  
Vol 32 (2) ◽  
pp. 519-558 ◽  
Author(s):  
Shuohui Yin ◽  
Tiantang Yu ◽  
Tinh Quoc Bui ◽  
Minh Ngoc Nguyen
Keyword(s):  
Nonlinear Analysis ◽  
Isogeometric Analysis ◽  
Volume Fraction ◽  
Functionally Graded ◽  
High Order ◽  
Basis Functions ◽  
Geometrically Nonlinear ◽  
Functionally Graded Plates ◽  
Geometrically Nonlinear Analysis ◽  
Content Type

Purpose – The purpose of this paper is to propose an efficient and accurate numerical model that employs isogeometric analysis (IGA) for the geometrically nonlinear analysis of functionally graded plates (FGPs). This model is utilized to investigate the effects of boundary conditions, gradient index, and geometric shape on the nonlinear responses of FGPs. Design/methodology/approach – A geometrically nonlinear analysis of thin and moderately thick functionally graded ceramic-metal plates based on IGA in conjunction with first-order shear deformation theory and von Kármán strains is presented. The displacement fields and geometric description are approximated with nonuniform rational B-splines (NURBS) basis functions. The Newton-Raphson iterative scheme is employed to solve the nonlinear equation system. Material properties are assumed to vary along the thickness direction with a power law distribution of the volume fraction of the constituents. Findings – The present model for analysis of the geometrically nonlinear behavior of thin and moderately thick FGPs exhibited high accuracy. The shear locking phenomenon is avoided without extra numerical efforts when cubic or high-order NURBS basis functions are utilized. Originality/value – This paper shows that IGA is particularly well suited for the geometrically nonlinear analysis of plates because of its exact geometrical modelling and high-order continuity.

Geometrically nonlinear analysis of two-dimensional structures using an improved smoothed particle hydrodynamics method

2015 ◽  
Vol 32 (3) ◽  
pp. 779-805 ◽  
Author(s):  
Jun Lin ◽  
Hakim Naceur ◽  
Daniel Coutellier ◽  
Abdel Laksimi
Keyword(s):  
Nonlinear Analysis ◽  
Smoothed Particle Hydrodynamics ◽  
Time Integration ◽  
Geometrically Nonlinear ◽  
Sph Method ◽  
Geometrically Nonlinear Analysis ◽  
Content Type ◽  
Particle Hydrodynamics ◽  
Sph Model ◽  
Smoothed Particle

Purpose – The purpose of this paper is to present an efficient smoothed particle hydrodynamics (SPH) method particularly adapted for the geometrically nonlinear analysis of structures. Design/methodology/approach – In order to resolve the inconsistency phenomenon which systematically occurs in the standard SPH method at the domain’s boundaries of the studied structure, the classical kernel function and its spatial derivatives were modified by the use of Taylor series expansion. The well-known tensile instabilities inherent to the Eulerian SPH formulation were attenuated by the use of the Total Lagrangian Formulation (TLF). Findings – In order to demonstrate the effectiveness of the present improved SPH method, several numerical applications involving geometrically nonlinear behaviors were carried out using the explicit dynamics scheme for the time integration of the PDEs. Comparisons of the obtained results using the present SPH model with analytical reference solutions and with those obtained using ABAQUS finite element (FE) commercial software, show its good accuracy and robustness. Practical implications – An additional application including a multilayered composite structure and involving buckling and delamination was investigated using the present improved SPH model and the results are compared to the FE results, they confirmed both the efficiency and the accuracy of the proposed method. Originality/value – An efficient 2D-continuum SPH model for the geometrically nonlinear analysis of thin and thick structures is proposed. Contrarily to the classical SPH approaches, here the constitutive material relations are used to link naturally the stresses and strains. The Total Lagrangian approach is investigated to alleviate the tensile instabilities problem, allowing at the same time to avoid the updating procedure of the neighboring particles search and therefore reducing CPU usage. The proposed approach is valid for isotropic and multilayered composites structures undergoing large transformations. CPU time savings and better results with the new 2D-continuum SPH formulation compared to the classical continuum SPH. The explicit dynamic scheme was used for time integration allowing a fast resolution algorithm even for highly nonlinear problems.

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